Competition for rank occurs whenever the outcome is a ranking, or league table, of the competitors. One can note that it is widespread throughout the plant and animal kingdoms, politics, higher education, and artificial contests. In the talk, I will describe a class of games that capture important aspects of this type of competition, and consider the problem of computing their Nash equilibria. An important background fact that motivated this study is the hardness of computing Nash equilibria of unrestricted games, which raises interest in more specific types of game for which the computational problem is tractable. I will also give a general overview of these hardness results, and how they arise.